Active vibration control of variable cross-section beams with piezoelectric actuating and sensing

Le résumé fourni par la source

Abstract To address the poor control performance of flexible beams with variable cross-sections, this study proposes an improved linear quadratic Gaussian with loop transfer recovery (LQG/LTR) active vibration control method optimized with an improved differential evolution (IDE) algorithm, which relies on piezoelectric actuation and sensing. Based on Euler–Bernoulli beam theory and piezoelectric dynamics theory, a coupled dynamic model of the flexible piezoelectric beam with variable cross-sections is established, and the finite-segment method is employed to determine the structure’s natural frequencies and modal shapes. For the problem of tuning the weight matrix parameters of the LQG/LTR controller, an IDE algorithm is introduced to optimize the controller parameters. Meanwhile, proportional-integral-derivative, fuzzy control, and traditional LQG controllers are employed as comparison methods. An experimental platform for active vibration control of a variable-cross-section piezoelectric flexible beam was constructed. Experiments were conducted on natural frequency testing, transient excitation, sinusoidal excitation, white noise excitation, and vibration control under dynamic conditions. The results show that the first two order natural frequencies obtained from theoretical calculations agree well with the experimental test results, with an error of less than 1%, verifying the accuracy of the established coupled dynamic model. Under different excitation conditions, the improved LQG/LTR controller demonstrated superior vibration suppression performance compared to other controllers, reducing vibration amplitude by 61%–78.5% under various excitation conditions. Furthermore, results from dynamic state experiments and extended structural experiments indicate that this control method can effectively suppress vibrations in variable-cross-section beams under dynamic excitation conditions and also exhibits a certain degree of vibration suppression for other flexible structures, demonstrating its potential for engineering applications. This study provides an effective method for modeling, optimizing, and experimentally validating active vibration control of variable-cross-section piezoelectric flexible structures.

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